SSC CGL Mock – Tier I Mock Test 10 – Section C · Quantitative Aptitude

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SSC CGL Mock – Tier I Mock Test 10 – Section C · Quantitative Aptitude – 25 questions, subject: Full Mock Tests. Every question has the correct answer with a one-line explanation; tap "Show Answer". Free practice for TNPSC, UPSC, SSC, Bank and RRB exams – Shanmugam IAS Academy, Coimbatore.

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1.  
Out of ₹ 18,000, one part is lent at 8% and the remainder at 12% simple interest per annum. Together they earn ₹ 1,760 in a year. Find the part lent at 8%.

Correct Answer: A [₹ 10,000]

Explanation:

0.08x + 0.12(18,000 − x) = 1,760 → 2,160 − 0.04x = 1,760 → x = 10,000.

2.  
A sum is divided among P, Q and R. P gets 2/3 of what Q and R together get, and Q gets 1/4 of what P and R together get. If R gets ₹ 3,850, what does Q get?

Correct Answer: A [₹ 1,925]

Explanation:

P = 2/5 of the total and Q = 1/5 of the total, so R = 2/5 → total = 9,625 → Q = 1,925.

3.  
P is 40% more efficient than Q. Q alone can do a job in 21 days. In how many days can P and Q together do it?

Correct Answer: D [8.75 days]

Explanation:

Rates 1.4 : 1 → together 2.4 times Q's rate → 21/2.4 = 8.75 days.

4.  
The length of a rectangular plot is increased by 15% and its breadth by 20%. By what percentage does its area increase?

Correct Answer: C [38%]

Explanation:

1.15 × 1.20 = 1.38 → area rises by 38%.

5.  
An acute angle θ has equal sine and cosine. Evaluate sin⁴ θ + cos⁴ θ.

Correct Answer: B [1/2]

Explanation:

θ = 45° → (1/√2)⁴ + (1/√2)⁴ = 1/4 + 1/4 = 1/2.

6.  
If tan A = 1/2 and tan B = 1/3, where A and B are acute, what is A + B?

Correct Answer: C [45°]

Explanation:

tan (A + B) = (1/2 + 1/3)/(1 − 1/6) = (5/6)/(5/6) = 1 → A + B = 45°.

7.  
The radii of two cylinders are in the ratio 2 : 3 and their heights in the ratio 5 : 3. What is the ratio of their volumes?

Correct Answer: B [20 : 27]

Explanation:

V ∝ r²h → 4 × 5 : 9 × 3 = 20 : 27.

8.  
A square pyramid has a base of side 14 cm and a vertical height of 24 cm. What is its total surface area?

Correct Answer: A [896 cm²]

Explanation:

Slant height = √(7² + 24²) = 25 → 196 + 4 × ½ × 14 × 25 = 896 cm².

9.  
Simplify: 1/(√6 + √5) + 1/(√5 + 2) + 1/(2 + √3)

Correct Answer: D [√6 − √3]

Explanation:

Rationalise each: (√6 − √5) + (√5 − 2) + (2 − √3) = √6 − √3.

10.  
Three alarms beep every 18, 24 and 32 minutes respectively. All three beep together at 8:00 a.m. At what time will they next beep together?

Correct Answer: D [12:48 p.m.]

Explanation:

LCM(18, 24, 32) = 288 min = 4 h 48 min after 8:00 a.m.

11.  
Given that a > 0 and the square of (a + 1/a) is 12, find a³ + 1/a³.

Correct Answer: B [18√3]

Explanation:

a + 1/a = 2√3 (a > 0) → a³ + 1/a³ = (a + 1/a)³ − 3(a + 1/a) = 24√3 − 6√3 = 18√3.

12.  
Simplify: (x⁴ − y⁴) ÷ [(x² + y²)(x − y)]

Correct Answer: C [x + y]

Explanation:

x⁴ − y⁴ = (x² + y²)(x + y)(x − y) → quotient = x + y.

13.  
For any two numbers a and b whose sum is 1, the expression a³ + b³ + 3ab always equals:

Correct Answer: A [1]

Explanation:

a³ + b³ = (a + b)³ − 3ab(a + b) = 1 − 3ab → a³ + b³ + 3ab = 1.

14.  
The diagonals of a rhombus are 18 cm and 24 cm. What is the length of each side?

Correct Answer: A [15 cm]

Explanation:

Diagonals bisect at right angles → side = √(9² + 12²) = 15 cm.

15.  
An equilateral triangle with 12 cm sides is drawn so that all three vertices lie on a circle. Find the radius of the circle.

Correct Answer: B [4√3 cm]

Explanation:

Answer: 4√3 cm. R = a/√3 = 12/√3 = 4√3 cm.

16.  
Diagram-basedIn the figure, AT is the tangent at A to the circle with centre O, and ∠BAT = 58°. Find ∠AOB.

Correct Answer: C [116°]

Explanation:

Angle between tangent and chord = angle in the alternate segment = 58°; the angle at the centre is twice that → 116°.

17.  
A price is cut by 25%, then by 20%, and then by 10%. What single percentage cut would have the same effect?

Correct Answer: D [46%]

Explanation:

0.75 × 0.8 × 0.9 = 0.54 → 46%.

18.  
By selling 33 metres of cloth, a shop gains the selling price of 11 metres. What is the gain per cent?

Correct Answer: C [50%]

Explanation:

SP(33) − CP(33) = SP(11) → CP(33) = SP(22) → gain = 11/22 = 50%.

19.  
A man who walks at three-quarters of his normal speed arrives at work 20 minutes late. How long does his walk normally take?

Correct Answer: D [60 minutes]

Explanation:

Time becomes 4/3 of usual → extra 1/3 of usual = 20 min → usual = 60 minutes.

20.  
The average salary of all the workers in a workshop is ₹ 12,000. The 7 technicians earn ₹ 18,000 each on average and the rest earn ₹ 9,000 each on average. How many workers are there in all?

Correct Answer: A [21]

Explanation:

7 × (18,000 − 12,000) = n × (12,000 − 9,000) → n = 14 → total = 21.

21.  

Directions (Q 71–74): The bar diagram shows the daily wages (₹) of the 60 workers of a factory, grouped in classes (fictional data; each class includes its lower limit but not its upper limit).

Bar chartHow many workers earn less than ₹ 400 a day?

Correct Answer: B [23]

Explanation:

Answer: 23. 8 + 15 = 23.

22.  
(Use the directions above – Q 71–74)
Bar chartWhat percentage of the workers earn ₹ 500 or more a day?

Correct Answer: B [25%]

Explanation:

Answer: 25%. (10 + 5)/60 × 100 = 25%.

23.  
(Use the directions above – Q 71–74)
Bar chartWhich wage class has the largest number of workers?

Correct Answer: C [₹ 400–500]

Explanation:

The tallest bar is 400–500 (22 workers).

24.  
(Use the directions above – Q 71–74)
Bar chartWhat is the ratio of the workers in the class 300–400 to those in the class 600–700?

Correct Answer: D [3 : 1]

Explanation:

Answer: 3 : 1. 15 : 5 = 3 : 1.

25.  
After 9 litres of a 7 : 5 milk-water mixture are taken out of a full can and replaced by water, the milk-water ratio becomes 7 : 9. How many litres does the can hold?

Correct Answer: A [36 litres]

Explanation:

Milk is now 7/16 of the can: 7/12 × (C − 9) = 7/16 × C → C = 36 litres.

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